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Sn-Zn alloy by artificial neural network

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Sn-Zn alloy by artificial neural networkby,SnZn,alloy,Alloy

    Sn-Zn alloy by artificial neural network J.Cent.SouthUniv.Techno1.(2010)17:715719

    DoI:10.1007/s11771-010-0545-x

    Springer

    Effectsofagingparametersonhardnessandelectricalconductivityof Cu--Cr-Sn-Znalloybyartificialneuralnetwork

    suJuanhua(苏娟华),JIAShuguo(贾淑果),RENFengzhang(任凤章)

    CollegeofMaterialsScienceandEngineering,HenanUniversityofScienceandTechnology,Luoyang471003,China

    CentralSouthUniversityPressandSpringerVerlagBerlinHeidelberg2010

    Abstract:InordertopredictandcontrolthepropertiesofCu--Cr-Sn?-Znalloy,amodelofagin

    gprocessesviaanartificialneural

    network(ANN)methodtomapthenon

    linearrelationshipbetweenparametersofagingprocessandthehardnessandelectrical conductivitypropertiesoftheCuCr-Sn

    Znalloywassetup.TheresultsshowthattheANNmodelisaveryusefulandaccuratetool forthepropertyanalysisandpredictionofagingCuCr-SnZnalloy.Agedat470510?

    for4-1h.theoptimalcombinationsof

    hardness110117(HV)andelectricalconductivity40.6

    37.7S/mareavailablerespectively.

    Keywords:Cu--Cr-Sn?-Znalloy;agingparameter;hardness;electricalconductivity;artificialneuralnetwork

    1Intr0ductiOn

    Inplasticpackagingapplicationofintegratedcircuit,

    copperalloysarethemostpopularleadflamealloysdue

    totheirhighthermalandelectricalconductivityaswell

    ashighstrengthf31.Thefunctionsof1eadflamein

    electronicpackingareprovidingchannelsforelectronic signalsbetweendevicesandcircuits,andfixingdevices oncircuitboards.Theaginghardeningprocessinthe fabricationofleadframecopperalloymakesitpossible togetbettermechanicalandelectricalproperties.XIE eta141studiedthemicrostructureandsolidification behaviorofCuNiSialloyswithfourdifierentCu

    contentssystematicallyundernear-equilibrium soliditicationconditions.HUANGandMA5]

    researchedtheprecipitationinCu.Ni.Si.Znalloyforlead frame.WANGeta16]analyzedtheinfluenceofDC

    electriccurrentonthehardnessofthermallyaged Cu.Cr-Zralloy.HUANGandMA71analyzedthe

    phasesinCu..Cr-Zralloy.Cu..Cr-Sn..Znalloyisa materialforleadflameswithexcellentsoflenresistivity, pressformability,electroplatability'bondabilityand solderability[8-9].Theagingprecipitatingprocessisan effectivewaytogethighperformanceforleadflame Cu.Cr-SnZnalloy101.Theprocesshasbeenmainly

    studiedempiricallybytria1..and..errormethodsotar.Itis importantanddesirabletosimulatetheeffectsofaging treatmentprocessesbynumerica1methodsinorderto analyzethem.Artificia1neuralnetwork(ANN)attempts toachievegoodperformanceviadenseinterconnection ofsimplecomputationalelements.Themodelsare composedofmanynonlinearcomputationalelements

    operatinginparallelandarrangedinapaRemofa biologicalneuralnetwork.ANNcanbeusedforthe mappingofinputtooutputdatawithoutknowingthe relationshipbetweenthosedataandcanbeappliedin

    optimumdesign,classificationandpredictionproblems 11121.SUandLI13]madeuseoftheANNmodel

    andimprovedtheLevenbergMarquardtalgorithmto

    analyzethehardnessofaleadflameCu.Cr.Zrcopper alloy.uetal[14]adoptedafullfactorialdesignmethod

    tocollectsampledatasets.InRef15],martensiteand

    austenitestarttemperaturesOfFe.basedshapememory alloyswerepredictedbyusingaback-propagation(BP) ANNthatusedgradientdescent1earningalgorithm. M0HAMMEDetal16]studiedthepotentialofusing

    neuralnetworkinpredictionofwearlOSSquantityof somealuminum-copper-siliconcarbidecomposite materials.Inthiswork,auniversalANNprogramwas designedonthebasisofBPtrainingalgorithmstomaD thecorrelationbetweenagingprocessparametersand propertiesandtopredicttheagingpropertiesinthe fabricationofhighperformanceCu0-36Cr-0.23Sn.

    0.15Zn(massfraction%1alloy.

    2InputandoutputvariablesofANN

    TheinputandoutputvariablesofANNarebasedon thebackgroundofaprocess.Thefollowingsareusedas Foundationitem:Project(2006AA03Z528)supportedbytheNationalHigh

    TechResearchandDevelopmentProgramofChina;Project(102102210174)

    supportedbytheScienceandTechnologyResearchProjectofHenanProvince,China;PTojec

    t(2OO8zDYYOO5)supponedbySlc)ecial

    FundforImportantForepartResearchinHenanUniversityofScienceandTechnology

    Receiveddate:2009——10——20;Accepteddate:2010——03——05

    Correspondingauthor:SUJuanhua,PhD,Professor;Tel:+86379

    64276860;E-mail:sujh@mail.haust.edu.cn 716J.

Cent.SouthUniv.Techno1.r2OLO)17:715719

    arethequantitiesofnodesinthefirstandthesecond hiddenlayers,respectively.SetNI=andadjust?2to

    ensurethatboththegeneralizationperformanceandthe rateoftheconvergencearesatisfactory.Atiermany timesoftria1.and.errorcomputationbytheANN program,perfecttopologies({2,4,9,2})ofthehardness andelectricalconductivityoutputsarefoundedforlead flameCuCrSnZnalloy.

    inputvariables:theagingtemperature(andtheaging time(,).Outputvariablesaredeterminedbythe propertiesacquirementofhardnessandelectrical conductivity.Theknowledgeofaspecificfieldis implicatedintheexistingtrainingsamples,soan appropriatedatasetwithgooddistributionissignificant forreliabletrainingandperformanceofneuralnetworks. Toensurereasonabledistributionandenough informationcontaininginthedataset,agingprocessesare coveredwithdifferentparameters.Theaging temperaturesare400,430,450,470,500,530,550,580 and600?,respectively;andtheagingtimesare0,5, l5,30,60,90,120,150,l80,240,300,and360min, respectively.

    Thealloyinvestigatedwaspreparedbysolution treatmentat920?forlhinargonatmosphereand

    waterquenching.Theagingtreatmentswerecarriedout inatubeelectricresistancefurnaceunderafluid atmosphereofargonwithtemperatureaccuracyof+5?.

    Theelectricalresistivitywasdeterminedbymeasuring theresistanceofsampleina1engthof100mmusinga

    ZY9987digitshowedohmmeter.Tbemicrohardnesswas measuredonanHVS-1000hardnesstesterundera1oad of100gandholdingfor10s.Everysamplewastested fivetimeswithanaccuracyof5%.Thesamplesfor

    transmissionelectronicmicroscope(TEM)analysiswere preparedbyconventionalelectropolishingmethod

    usinganelectrolyteofV(I-1NO3):CH2OH)=I:3.The electronmicroscopemeasurementwascarriedoutby usinganH-800TEMat200kV

    3Hiddenlayersandneurons

    Hiddenlayersperformabstractfunctions.namely, theycanextractcharacteristicknowledgeimplicatedin inputdata.Soitisthehiddenlayersthatgiveneural networkstheabilitytorobustlydealwithnonlinearand complexproblems.However,differentalgorithmsofBP networkshavedifferentlimitationsinpractice.For instance.itisdifficultforasinglehidden.1ayernetwork

    toimproveitscloseness.of-fitifithastoofewhidden nodes;whileexcessivemanyhiddennodesenableitto memorize(over-fit)thetrainingdataset,whichproduces poorgeneralizationperformance.Atpresentthereisnota validanalysisformulafordesigninghiddenlayersandit isanarttodecidethequantityofnodesperhiddenlayer, soatradeoffexistsbetweengeneralizationperformance andthecomplexityoftrainingprocedurewhendesigning thetopologyofaneuralnetwork.

    Inthisworka1otofcomputationalinstancesshow thattwohidden.1ayerneuralnetworksaresuitable.N (nottoogreat)isthedimensionofinputlayers,N1and?2

    4BPneuralnetworks

BP,whichisoneofthemostfamoustraining

    algorithmsformultilayerperception,isagradient

    descenttechniquetominimizetheerrorforparticular trainingpattern.Theweightsoftheneuronsare iterativelyadjustedinaccordancewiththeerror correctionruleuntiltheoutputforaspecificnetworkis closetothedesiredoutput[17191.

    Eachinputunitoftheinputlayerreceivesinput signalxjandbroadcaststhissignaltoallunitsinthe hiddenlayer.Eachhiddenunitsumsitsweightedinput signalandappliesitsactivationfunctiontocompute outputsigna1.

    Y=_(?)(1)

    wherew/jistheweightfrominputunittohiddenunitYi TheoutputsignalofhiddenunitYissenttoallunitsin theoutputlayer.EachoutputunitOlsumsitsweighted inputsignalandusesitsactivationfunctiontocompute itsoutputsigna1.

    ol=_(?o)ityi)(2)

    whereO)ilistheweightfromhiddenunitYftooutputunit O1.Theactivationfunctionusedinthisworkisalogistic sigmoidfunctiondefinedas

    1

    f=——

    1+e

    (3)

    TheBPtrainingalgorithmisaniterativegradient descentalgorithm,whichisdesignedtominimizethe sumofsquareerror(andaveragesallpatterns,is calculatedasfollows:

E:?()(4)

    wheretlisthedesiredoractualoutput:ando,isthe predictedoutputforthe/thpattern.

    ThetrainingprocedureisshowninFig.1.Itreveals thatthetrainingerrorisalwaysreducedduringthe trainingprocedure.Thetrainingerrorishardlychanged aftertheepochsareupto500times.

    J.Cent.SouthUniv.Techno1.(2olo)17:715-719717 Numberofepoch

    Fig.1Trainingprocedureofneuralnetworkmode(Performance isO.0512202,

    5Resultsanddiscussion

    Fig.2revealstherelationshipbetweenthepredicted valuesfromthetrainedneuralnetworkandthetested datatotestthegeneralizationperformanceofthetrained networks.Verygoodagreementsbetweenthemare achieved.whichindicatesthatthetrainednetworksareof optimalgeneralizationperformance.Thisalso demonstratesthat,asatypicaldataminingtechnique, SampleNo

    SampleNo

    Fig.2Resultsofvalidatinggeneralization:(a)Electrical conductivity;(b)Hardness

    neura1networkcanfindthebasicpatteminformation impliedinagreatnumberofexperimentaldata,extract usefulrulesandthenusetheserulesforobtaining reasonablepredictedresults.

    Bvusingthedomaininformationstoredinthe

    trainednetworks,threedimensionalgraphisdrawnin

    Fig.3,whichpresentsmuchmoreprofessional

    informationabouttherelationshipbetweenhardnessand agingproperties.

    6

    Fig.3HardnessofCuCrSnZnalloywithregardto

    temperatureandtime

    Fig.3revealsthatthetimetoreachthepeak

    hardnessdecreaseswithincreasingtemperature.Withthe enhancementofthetemperature.theinitia1kineticofthe precipitationiShigher,whichleadstoshortertimeto reachthepeakhardness20].Forexample,agingat470

    5l0?f0r4-1hthemaximumhardnesscanbe

    obtainedfroml10to117rHV1.Atthepeakhardnessthe ful1precipitationisavailableandthehardeningeffectis optimum.

    TheTEMimageoftheprecipitatesiSshownin

    Fig.4.ThemicrostructuresofCu.Cr.SnZnalloyarethe

    finelydispersedprecipitatesinCumatrix,havingasize of10-40nm,asshowninFig.4.Thesefineprecipitates togetherwithCumatrixgiverisetopeakhardness.The hardnessincreasefollowstheempiricalOrowan relationship:

    Fig.4TEMimageofCuCrSn-Znalloyagedat500?for

    l5min

    >}{一???IIpJ}{

    I__I1.?>u10u一矗u【』u0

    >ZJs?0I}{

    718J.

    Cent.SouthUniv.Techno1.(2010)17:715719

    conformstothevariationofresistivityatadefiniteaging temperature.Thelongertheagingtime,thelessthe

    numberofthesupersaturatedvacancies,themoreslowly theprecipitationprocess.

    f=2}R

    whereAristheincreaseinshearstress;kistheconstant; fisthevolumefractionofprecipitates;andRdenotesthe diameterofprecipitates.BymeansoftheTEManalysis ofFig.4,thevolumefractionofprecipitatesis30%

    40%.Thehigherthevolumefractionofprecipitates.the smallerthesizeoftheprecipitates,thegreaterthe?the

    greaterthehardnessofthealloy.

    Theelectrica1conductivityincreaseswiththe increaseoftimeandtemperature.asshowninFig.5. Agedat510?for1htheelectrica1conductivityis

    37.7S/m.Thehighestconductivityreaches40.8S/mat 600?for6h.Thehighertemperatureand1ongertime bringaboutmoreprecipitates,whichleadstothe conductivityalmostreaching40.6S/m,asshowninFig.5 Thegrowthofprecipitatesreducesthecontentsofsolute atominmatrixandresultsinacontinuousincreasein electricalconductivityduringtheagingprocess.So,the electrica1conductivityinCuCrSn.Zn1eadflamealloy

    remainsahigherlevelatahighertemperatureandlonger timeagingprocess.

    6Conclusions

    (1)Aneuralnetworkmodelofagingprocessesis builtforCu0.36Cr.0.23Sn0.15Znalloy.Highprecision

    aswellasgoodgeneralizationperformanceofthemodel isdemonstrated.

    r2)Bythedomainknowledgestoredinthetrained networks.three.dimensionalgraphisobtained.Withthe

    helpoftheknowledgerepositorystoredinthetrained network.importantfoundationislaidfortheoptimally controllingandpredictingtheagingpropertiesof Cu.0.36Cr-0.23Sn.0.15Znalloy.

    (3)Agingat470510?for4lh,theoptimal

    combinationsofhardnessandconductivityofthealloy are1l0-1l7(HV1and40.6-37.7S/m.respectively. References

    [2

    [3

    [4

    Fg?5tri..?ndu.iVty.cu'sn.Zna.ywimregar0f5Jtotemperatureandtime

    6]

    UponagingthesolidifiedCu.CrSn.Znalloyfirst underwenttheprecipitationprocessduetoitsextended super-saturationlimitandmuchmorecrystaldefects.It istheprecipitationofsupersaturatedsolidsolutionthat resultsjntheinitia1sharpjncreaseofconductivity.The precipitationproceedsthroughdiffusingthesoluteatoms withtheaidofvacancies.Thevacancieswithhigher concentrationinthesolidifledalloyshiRrapidlyatthe initialstageofagingprocess,andthedecayofthemcan beexpressedbythefollowingequation[21:

    =Noexp(-ant)(6)

    whereNisthequantityofvacancy;nisthenumberof vacancysitesthatkeepconstantuponaging;aisthe constantatadefiniteagingtemperature;tistheaging time;andNoisthevacancyquantityofsupersaturated solidsolution.Itisnotedthatthedecayofvacancies [7]

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